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A026856 a(n) = T(2n+1,n+3), T given by A026736.

%I A026856 #18 Sep 08 2022 08:44:49
%S A026856 1,7,36,166,729,3125,13229,55637,233227,976271,4085016,17096524,
%T A026856 71590557,299993227,1258076725,5280194087,22178492943,93226087229,
%U A026856 392144055809,1650570659359,6951524807631,29292822272697,123496979334851
%N A026856 a(n) = T(2n+1,n+3), T given by A026736.
%H A026856 G. C. Greubel, <a href="/A026856/b026856.txt">Table of n, a(n) for n = 2..1000</a>
%F A026856 G.f.: (x^2 * C(x)^6)/(1 - x/sqrt(1-4*x)) where C(x) = g.f. for Catalan numbers A000108. - _David Callan_, Jan 16 2016
%F A026856 a(n) ~ (3 - sqrt(5))^6 * (2 + sqrt(5))^(n+3) / (64*sqrt(5)). - _Vaclav Kotesovec_, Jul 18 2019
%t A026856 CoefficientList[Series[(1-Sqrt[1-4x])^6/(64*x^6*(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* _David Callan_, Jan 16 2016 *)
%o A026856 (PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^6/(64*x^6*(1-x/sqrt(1-4*x))) ) \\ _G. C. Greubel_, Jul 21 2019
%o A026856 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^6/(64*x^6*(1-x/Sqrt(1-4*x))) )); // _G. C. Greubel_, Jul 21 2019
%o A026856 (Sage) ((1-sqrt(1-4*x))^6/(64*x^6*(1-x/sqrt(1-4*x)))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 21 2019
%Y A026856 Cf. A000108, A026736.
%K A026856 nonn
%O A026856 2,2
%A A026856 _Clark Kimberling_